Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
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abstract
We evaluate analytically higher terms of the epsilon-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g-2 in QED up to the transcendentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
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Magic Relations and Critical Varieties of Feynman Integrals
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
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On the spanning cuts consistency problem in the IBP reductions of Feynman integrals
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.